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Supercompact Extender Based Magidor-Radin Forcing
Carmi Merimovich
The extender based Magidor-Radin forcing is being generalized to supercompact type extenders.
Some applications of Supercompact Extender Based Forcings to HOD
Moti Gitik, Carmi Merimovich
Supercompact extender based forcings are used to construct models with HOD cardinal structure different from those of V. In particular, a model with all regular uncountable cardina…
Wider Thin-Very Tall Superatomic Boolean Algebras
Carmi Merimovich
For each regular cardinal k > w we show the consistent existence of a thin very tall superatomic Boolean algebra of width k.
Prikry On Extenders, Revisited
Carmi Merimovich
We present a modification to the Prikry on Extenders forcing notion allowing the blow up of the power set of a large cardinal, change its cofinality to omega without adding bounded…
A Power Function with A Fixed Finite Gap Everywhere
Carmi Merimovich
We give an application of our extender based Radin forcing to cardinal arithmetic. Using a preparation forcing and interleaving of Cohen and Levy forcings in the normal Radin seque…
Extender Based Radin Forcing
Carmi Merimovich
We define extender sequences, generelizing measure sequences from Radin Forcing. Using the extender sequences we combine Gitik-Magidor forcing for adding many Prikry sequences with…